A good first step is often to see what the differences and ratios are. But since 13 is prime and 25 isn't a multiple, this is probably not a purely multiplicative sequence. Also, I don't "see" any obvious evidence of squaring or cubing (such as numbers related to 4, 9, 16, 25,... or 8, 27, 64,...).

The differences, though, look promising: 13 - 5 = 8, 25 - 13 = 12, 41 - 25 = 16, 61 - 41 = 20. For each of these, the difference was a multiple of four. In fact, the first difference was twice four, the second difference was three times four, and so forth.

So see if you can come up with a formula for this difference, in terms of the n-th term.

Then see if you can develop a formula for the entire n-th term, both the added multiple of four and the original value.

Anyway, using the techniques in the lesson in the link provided earlier, you'll have already proven to yourself that the multipliers follow some quadratic rule. For the first three terms (and thus the first three values of "n'), the multipliers are then given by: